Abstract

The results of the application of previously developed techniques to the analysis of the Petrov type III solutions to the vacuum Einstein equations are presented. The procedure involves the computer aided analysis of the Einstein‐Petrov equations to the extent that the functions uniquely and invariantly generating all local analytic solutions are determined. For the case of type III it is shown that, relative to a given fixed point in the manifold, all local analytic solutions are uniquely and invariantly determined by six arbitrary analytic functions of one variable and six others of two variables. These functions, called generating functions, thus provide a representation of all such solutions and may be used for the study of the structure of the family of Einstein empty space metrics.